《人工智能基礎(chǔ)》實(shí)驗報告-實(shí)驗名稱啟發(fā)式搜索算法

1、實(shí)驗名稱:啟發(fā)式搜索算法專業(yè)班級學(xué)號姓名1、實(shí)驗環(huán)境Visual C+ 6. 02、實(shí)驗?zāi)康暮鸵?復(fù)述問題)使用啟發(fā)式算法求解8數(shù)碼問題編制程序?qū)崿F(xiàn)求解8數(shù)碼問題A*算法，采用估價函數(shù)f(n) =d(n) +p (n)其中：d(n)是搜索樹中結(jié)點(diǎn)n的深度:w(n)為節(jié)點(diǎn)n的數(shù)據(jù)庫中錯放的旗子個數(shù)； p(n)為結(jié)點(diǎn)n的數(shù)據(jù)庫中每個棋子與其目標(biāo)位置之間的距離總和。分析上述(1)中兩種估價函數(shù)求解8數(shù)碼問題的效率差別，給出一個是p(n)的 上界h(n)的定義，并測試該估價函數(shù)是否使算法失去可采納性。實(shí)驗?zāi)康模菏炀氄莆諉l(fā)式搜索A*算法及其可采納性。3、解題思路、代碼1解題思路八數(shù)碼問題的求解算法盲

2、目搜索寬度優(yōu)先搜索算法、深度優(yōu)先搜索算法啟發(fā)式搜索啟發(fā)式搜索算法的基本思想是：定義一個評價函數(shù)f,對當(dāng)前的搜索狀態(tài)進(jìn)行評估, 找出一個最有希望的節(jié)點(diǎn)來擴(kuò)展。先定義下面幾個函數(shù)的含義：f* (n) =g* (n) +h* (n) (1)式中g(shù)*(n)表示從初始節(jié)點(diǎn)s到當(dāng)前節(jié)點(diǎn)n的最短路徑的耗散值：h*(n)表示從當(dāng)前 節(jié)點(diǎn)n到目標(biāo)節(jié)點(diǎn)g的最短路徑的耗散值，f*(n)表示從初始節(jié)點(diǎn)s經(jīng)過n到目標(biāo)節(jié)點(diǎn)g 的最短路徑的耗散值。評價函數(shù)的形式可定義如(2)式所示：f (n) =g (n) +h (n) (2)其中n是被評價的當(dāng)前節(jié)點(diǎn)。f (n)、g (n)和h (n)分別表示是對f* (n)、g*(n)

3、和h* (n) 3 個函數(shù)值的估計值。利用評價函數(shù)f(n)=g(n)+h(n)來排列OPEN表節(jié)點(diǎn)順序的圖搜索算法稱為算法A。在 A算法中,如果對所有的x, h(x)=h*(x) 成立，則稱好h(x)為h*(x)的下界，它 表示某種偏于保守的估計。采用h*(x)的卜界h(x)為啟發(fā)函數(shù)的A算法，稱為A*算法針對八數(shù)碼問題啟發(fā)函數(shù)設(shè)計如下：F (n) =d (n) +p (n) (4)其中A*算法中的g(n)根據(jù)具體情況設(shè)計為d(n)，意為n節(jié)點(diǎn)的深度，而h(n)設(shè)計 為p(n),意為放錯的數(shù)碼與正確的位置距離之和。由于實(shí)際情況中，一個將牌的移動都是單步進(jìn)行的，沒有交換拍等這樣的操作。所 以要把

4、所有的不在位的將牌，移動到各自的目標(biāo)位置上，至少要移動從他們各自的位置 到目標(biāo)位置的距離和這么多次，所以最有路徑的耗散值不會比該值小，因此該啟發(fā)函數(shù) h(n)滿足A*算法的條件。初始狀態(tài)目標(biāo)狀態(tài) 吵O O3.2代碼#include#include#include八數(shù)碼狀態(tài)對應(yīng)的節(jié)點(diǎn)結(jié)構(gòu)體struct Node(int s33;/保存八數(shù)碼狀態(tài)，0代表空格 int f,g;啟發(fā)函數(shù)中的f和g值 struct Node * next;struct Node *previous;/保存其父節(jié)點(diǎn)；int open_N=0; /記錄Open列表中節(jié)點(diǎn)數(shù)目八數(shù)碼初始狀態(tài)int inital_s33=2.8

5、.3,1.6.4,7,0,5；八數(shù)碼目標(biāo)狀態(tài)int final_s33=(1,2,3,8,0,4,7,6,5)；/添加節(jié)點(diǎn)函數(shù)入II,方法：通過插入排序向指定表添加/void Add_Node( struct Node *head, struct Node *p)(struct Node *q;if(head-next)/考慮鏈表為空( q = head-next;if(p-f next-f)(/考慮插入的節(jié)點(diǎn)值比鏈表的第一個節(jié)點(diǎn)值小 p-next = head-next;head-next = p;else (while(q-next)考慮插入節(jié)點(diǎn)x,形如a= x f f 11 q-f =

6、p-f) & (q-next-f p-f 11 q-next-f = p-f)( p-next = q-next;q-next = p;break;q = q-next;if(q-next = NULL) 考慮插入的節(jié)點(diǎn)值比鏈表最后一個元素的值更大 q-next = p;else head-next = p;/刪除節(jié)點(diǎn)函數(shù)入11void del_Node(struct Node * head, struct Node *p )struct Node *q; q = head;while(q-next)if(q-next = p)( q-next = p-next; p-next = NULL;

7、 if(q-next = NULL) return;/ free(p);q = q-next;/判斷兩個數(shù)組是否相等函數(shù)入11/ -int equal(int sl33, int s233)(int iJ/flag=0;for(i=0; i 3 ; i+)for(j=0; jnext;int flag = 0;while(q)if(equal(q-s,s) (flag=l;Old_Node-next = q;return 1;else q = q-next;if(!flag) return 0;)/計算p(n)的函數(shù)入口其中p(n)為放錯位的數(shù)碼與其正確的位置之間距離之和具體方法：放錯位的數(shù)碼

8、與其正確的位置對應(yīng)卜標(biāo)差的絕對值之和/int wrong_sum(int s33)int i,j,fi,fj,sum=0;for(i=0; i3; i+)for(j=0; j3; j+)(for(fi=0; fi3; fi+)for(fj=0; fj3; fj+)if(final_sfifj =siU)(sum += fabs(i - fi) + fabs(j - fj);break;return sum;/獲取后繼結(jié)點(diǎn)函數(shù)入口檢查空格每種移動的合法性，如果合法則移動空格得到后繼結(jié)點(diǎn)/int get_successor(struct Node * BESTNODE, int direction

9、, struct Node *Successor)擴(kuò)展BESTNODE,產(chǎn)生其后繼結(jié)點(diǎn)SUCCESSOR(int i,j,i_0,j_0,temp;for(i=0; i3; i+)for(j=0; jsij = BESTNODE-sij;獲取空格所在位置for(i=0; i3; i+)for(j=0; jsij = 0)i_0 = i; j_0 = j;break;switch(direction)case 0: if(i_0-l)l)(temp = Successor-si_0j_0;Successor-si_0j_0 = Successor-si_0-l j_0;Successor-si_

10、0-l j_0 = temp;return 1;else return 0;case 1: if(j_Ol)l)temp = Successor-si_0j_0;Successor-si_0j_0 = Successorsi_0j_0-1;Successor-si_0j_0-l = temp;return 1;else return 0;case 2: if( (j_0+l)si_0j_0;Successor-si_0j_0 = Successor-si_0j_0+l;Successor-si_0j_0+l = temp;return 1;else return 0;case 3: if(i_

11、0+l)si_0j_0;Successor-si_0j_0 = Successorsi_0+Ij_0;Successor-si_0+lj_0 = temp;return 1;else return 0;從OPen表獲取最佳節(jié)點(diǎn)函數(shù)入I 1struct Node * get_BESTNODE(struct Node *Open)return Open-next;/輸出最佳路徑函數(shù)入11/void print_Path(struct Node * head)(struct Node *q, int ij,count=l;p = (struct Node *)malloc(sizeof(struct

12、 Node);通過頭插法變更節(jié)點(diǎn)輸出次序p-previous = NULL;q = head;while(q)ql = q-previous;q-previous = p-previous;p-previous = q;q = qi;q = p-previous;while(q)if(q = p-previous)printf(A數(shù)碼的初始狀態(tài):n)；else if(q-previous = NULL)printf(,八數(shù)碼的目標(biāo)狀態(tài)：nH)； else printf(八數(shù)碼的中間態(tài)dn,count+);for(i=0; i3; i+)for(j=0; jsij);if(j = 2)print

13、f(”n”);printf(,f=%d/ g=%dnn,q-f,q-g);q = q-previous;)A*子算法入I I:處理后繼結(jié)點(diǎn) void sub_A_algorithm(struct Node * Open, struct Node * BESTNODE, struct Node * Closed,struct Node *Successor)(struct Node * Old_Node = (struct Node *)malloc(sizeof(struct Node);Successor-previous = BESTNODE;/建立從 successor 返回 BESTN

14、ODE 的指針Successors = BESTNODE-g + 1;/計算后繼結(jié)點(diǎn)的 g 值檢查后繼結(jié)點(diǎn)是否己存在于Open和Closed表中，如果存在：該節(jié)點(diǎn)記為old_Node,比較 后繼結(jié)點(diǎn)的g值和表中old_Node節(jié)點(diǎn)g值，前者小代表新的路徑比老路徑更好，將0ld_Node的父節(jié)點(diǎn)改為BESTNODE,并修改 其f, g值，后者小則什么也不做。即不存在Open也不存在Closed表則將其加入OPen表，并計算其f值if( exit_Node(Open, Successors, Old_Node)(if(Successor-g g)Old_Node-next-previous = B

15、ESTNODE;/將 Old_Node 的父節(jié)點(diǎn)改為 BESTNODEOld_Node-next-g = Successor-g;/修改 g 值Old_Node-next-f = Old_Node-g + wrong_sum(Old_Node-s);修改 f 值/J V.ZZ2ZZZZZZZZZZZ2ZZZdel_Node(Open, Old_Node);Add_Node(Open, Old_Node);)else if( exit_Node(Closed, Successors, Old_Node)(if(Successor-g g)Old_Node-next-previous = BEST

16、NODE;Old_Node-next-g = Successor-g;Old_Node-next-f = Old_Node-g + wrong_sum(Old_Node-s);/J V.ZZ2ZZZZZZZZZZZ2ZZZdel_Node(Closed, Old_Node);Add_Node(Closed, Old_Node);)else (Successor-f = Successor-g + wrong_sum(Successor-s);Add_Node(Openz Successor);open_N+;)A*算法入口八數(shù)碼問題的啟發(fā)函數(shù)為：f(n)=d(n)+p(n)其中A*算法中的g(

17、n)根據(jù)具體情況設(shè)計為d(n),意為n節(jié)點(diǎn)的深度，而h(n)設(shè)計為p(n),意為放錯的數(shù)碼與正確的位置距離之和/void A_algorithm(struct Node * Open, struct Node * Closed) A*算法int i,j;struct Node * BESTNODE, *inital, * Successor;inital = (struct Node * )malloc(sizeof(struct Node);初始化起始節(jié)點(diǎn)for(i=0; i3; i+)for(j=0; jsij = inital_sij;inital-f = wrong_sum(inita

18、l_s);inital-g = 0;inital-previous = NULL;inital-next = NULL;Add_Node(Open, inital);把初始節(jié)點(diǎn)放入 OPEN 表open_N+;while(l)if(open_N = 0)(printf(,failure!H); return;else (BESTNODE = get_BESTNODE(Open);/從 OPEN 表獲取 f 值最小的 BESTNODE,將其 從OPEN表刪除并加入CLOSED表中del_Node(Openz BESTNODE);open_N-；Add_Node(Closed, BESTNODE)

19、;if(equal(BESTNODE-s, finals) /判斷 BESTNODE 是否為目標(biāo)節(jié)點(diǎn)printf(success!n);print_Path(BESTNODE);return;針對八數(shù)碼問題，后繼結(jié)點(diǎn)Successor的擴(kuò)展方法：空格(二維數(shù)組中的0)上 下左右移動，判斷每種移動的有效性，有效則轉(zhuǎn)向A*子算法處理后繼節(jié)點(diǎn)，否則進(jìn)行下一 種移動else(Successor = (struct Node * )malloc(sizeof(struct Node); Successor-next = NULL;if(get_successor(BESTNODE, 0, Success

20、or)sub_A_algorithm( Open, BESTNODE, Closed, Successor);Successor = (struct Node * )malloc(sizeof(struct Node); Successor-next =NULL;if(get_successor(BESTNODE, 1, Successor)sub_A_algorithm( Open, BESTNODE, Closed, Successor);Successor = (struct Node * )malloc(sizeof(struct Node); Successor-next = NUL

21、L;if(get_successor(BESTNODE, 2, Successor)sub_A_algorithm( Open, BESTNODE, Closed, Successor);Successor = (struct Node * )malloc(sizeof(struct Node); Successor-next = NULL;if(get_successor(BESTNODE, 3, Successor)sub_A_algorithm( Open, BESTNODE, Closed, Successor);)main()函數(shù)入11定義Open和Closed列表。Open列表：保存待檢查節(jié)點(diǎn)。Closed列表：保存不需要再檢 查的節(jié)點(diǎn)void main()(struct Node * Open = (struct Node